Estimating brain conductivities and dipole source signals with EEG arrays

Techniques based on electroencephalography (EEG) measure the electric potentials on the scalp and process them to infer the location, distribution, and intensity of underlying neural activity. Accuracy in estimating these parameters is highly sensitive to uncertainty in the conductivities of the head tissues. Furthermore, dissimilarities among individuals are ignored when standardized values are used. In this paper, we apply the maximum-likelihood and maximum a posteriori (MAP) techniques to simultaneously estimate the layer conductivity ratios and source signal using EEG data. We use the classical 4-sphere model to approximate the head geometry, and assume a known dipole source position. The accuracy of our estimates is evaluated by comparing their standard deviations with the Crame/spl acute/r-Rao bound (CRB). The applicability of these techniques is illustrated with numerical examples on simulated EEG data. Our results show that the estimates have low bias and attain the CRB for sufficiently large number of experiments. We also present numerical examples evaluating the sensitivity to imprecise assumptions on the source position and skull thickness. Finally, we propose extensions to the case of unknown source position and present examples for real data.

I. Introduction

The PROBLEM of dipole source localization and signal estimation is of great interest in neuroscience. It has applications in areas such as clinical sciences and brain research [1]. Techniques based on electroencephalography (EEG) measure the electric potentials on the scalp and process them to infer the location and signal of the underlying neural activity. Solution to this inverse problem requires knowledge of the conductivities of the different layers in the head. It has been shown that accuracy of estimating the source parameters is highly sensitive to the uncertainty in the conductivities of most of the head tissues [2]. These conductivities are typically obtained by direct measurements of in vivo and in vitro samples of the tissues involved [3]. Then, dissimilarities in the conductivities among individuals are ignored. Other methods such as impedance tomography [4], [5], and magnetic resonance using current density imaging [6] allow individual estimation, but they require each patient to be a subject of a study for estimating his/her tissues' conductivities before, and in addition to, the EEG measurements. Recently, magnetic resonance diffusion-weighted imaging techniques have been developed to estimate conductivities on an individual basis [7]. Simultaneous magnetoencephalography (MEG) and EEG analysis has been used to derive “equivalent” conductivity estimates that improve the estimation of dipole source parameters [8].